Skip to main content

Stochastic Quantization and Gauge Fixing in Gauge Theories

  • Conference paper
Book cover Stochastic Methods and Computer Techniques in Quantum Dynamics

Part of the book series: Acta Physica Austriaca ((FEWBODY,volume 26/1984))

Abstract

These lectures were supposed to focus on a specific non-compact lattice gauge model with a peculiar “stochastic” gauge fixing invented by Zwanziger. But to put this model into perspective I find it appropriate to widen the scope of these lectures somewhat.

Lectures given at the XXIII. Internationale Universitätswochen für Kernphysik, Schladming, Austria, February 20-March 1, 1984.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ph. Blanchard, these proceedings.

    Google Scholar 

  2. L. Streit, these proceedings.

    Google Scholar 

  3. P. Zoller, these proceedings.

    Google Scholar 

  4. E. Nelson, Phys. Rev. 150 (1966) 1079; Dynamical Theories of Brownian Motion (Princeton University Press, 1967); “Connection Between Brownian Motion and Quantum Mechanics”, in Lecture Notes in Physics, vol. 100 (Springer-Verlag, Berlin-Heidelberg-New York, 1979) (Einstein Symposium Berlin).

    Article  ADS  Google Scholar 

  5. G. Jona-Lasinio, “Stochastic Processes and Quantum Mechanics”, talk given at the Colloque en I’Honneur de L. Schwartz, Ecole Polytechnique, June 1983, to appear in Asterisque.

    Google Scholar 

  6. C. de Witt-Morette and D. Elworthy, Phys. Rep. 77 (1981).

    Google Scholar 

  7. F. Guerra and P. Ruggiero, Lett. Nuov. Cim. 31 (1973) 1022.

    Google Scholar 

  8. F. Guerra, Phys. Rep. 11 (1981) 263.

    Article  ADS  MathSciNet  Google Scholar 

  9. B. Simon, Functional Integration in Quantum Physics (Academic Press, New York-San Francisco-London, 1979).

    Google Scholar 

  10. G. Parisi and Y.S. Wu, Scientia Sinica 24 (1981) 483.

    MathSciNet  Google Scholar 

  11. E. Gozzi, Phys. Lett. 129B (1983) 432, (Err. 134B (1983) 477); Phys. Lett. 130B (1983) 83; Phys. Rev. D28 (1983) 1922; “The Onsager’s Principle of Microscopic Reversibility and Supersymmetry”, CCNY-HEP-83/16;

    ADS  MathSciNet  Google Scholar 

  12. R. Kirschner, “Quantization by Stochastic Relaxation Processes and Supersymmetry”, KMU-HEP 84–01.

    Google Scholar 

  13. G. Parisi and N. Sourlas, Nucl. Phys. B206 (1982) 321; Phys. Rev. Lett. 43 (1979) 744.

    Article  ADS  MathSciNet  Google Scholar 

  14. P. Walters, Introduction to Ergodic Theory (Springer- Verlag, Berlin-Heidelberg-New York, 1982).

    Book  MATH  Google Scholar 

  15. A. Guha and S.C. Lee, Phys. Rev. D27 (1982) 2412; Phys. Lett. 134B (1984) 216.

    ADS  MathSciNet  Google Scholar 

  16. D. Zwanziger, Nucl. Phys. B192 (1981) 259; Phys. Lett. 114B (1982) 337; Nucl. Phys. B209 (1982) 336.

    Article  ADS  MathSciNet  Google Scholar 

  17. S. Helgasson, Differential Geometry and Symmetric Spaces (Academic Press, New York-San Francisco-London, 1962), Chapter X, Prop. 2.1.

    Google Scholar 

  18. N.D. Hari Dass, P.G. Lauwers and A. Patkos, Phys. Lett. 124B (1983) 387; Phys. Lett. 130B (1983) 292.

    ADS  MathSciNet  Google Scholar 

  19. L. Baulieu and D. Zwanziger, Nucl. Phys. B193 (1981) 163.

    Article  ADS  MathSciNet  Google Scholar 

  20. I.M. Singer, Comm. Math. Phys. 60 (1978) 7

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. O. Babelon and C.-M. Viallet, Phys. Lett. 85B (1979) 246.

    ADS  MathSciNet  Google Scholar 

  22. M. Creutz, I. Muzinich, T. Tudron, Phys. Rev. D19 (1979) 531.

    ADS  Google Scholar 

  23. A. Chodos and V. Moncrief, J. Math. Phys. D19 (1980) 364.

    Article  ADS  MathSciNet  Google Scholar 

  24. H. Flanders, Differential Forms with Applications to the Physical Sciences (Academic Press, New York-London, 1963).

    MATH  Google Scholar 

  25. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Non-selfadjoint Operators (American Mathematical Society Translations, Providence, R.I., 1969).

    Google Scholar 

  26. E. Seller, I.O. Stamatescu and D. Zwanziger, “Monte Carlo Simulations of Non-Compact QCD with Stochastic Gauge Fixing”, Nucl. Phys. B, in print.

    Google Scholar 

  27. E. Seller, I.O. Stamatescu and D. Zwanziger, “Numerical Evidence for a Barrier at the Gribov Horizon”, Nucl. Phys. B, in print.

    Google Scholar 

  28. I.O. Stamatescu, U. Wolff and D. Zwanziger, Nucl. Phys. B225[FS9] (1983) 377.

    Article  ADS  Google Scholar 

  29. A. Patrascioiu, E. Seller and I.O. Stamatescu, Phys. Lett. 107B (1981) 364.

    ADS  Google Scholar 

  30. F. Guerra and R. Marra, “Discrete Stochastic Variational Principles ana Quantum Mechanics”, preprint Università di Roma, 1983.

    Google Scholar 

  31. H.P. McKean, Stochastic Integrals (Academic Press, New York-San Francisco-London 19 69);

    MATH  Google Scholar 

  32. N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes (North Holland Publishing Co., Amsterdam-Oxford-New York, 1981).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Seiler, E. (1984). Stochastic Quantization and Gauge Fixing in Gauge Theories. In: Mitter, H., Pittner, L. (eds) Stochastic Methods and Computer Techniques in Quantum Dynamics. Acta Physica Austriaca, vol 26/1984. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8780-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-8780-7_11

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-8782-1

  • Online ISBN: 978-3-7091-8780-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics